Glossary
Z-score
Definition
A z-score says how many standard deviations a score sits above or below the mean. A z of 0 is exactly average, +1 is one standard deviation above and -2 is two below. On the standard IQ scale, z equals the IQ minus 100, divided by 15.
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Why it matters for IQ scores
The z-score is the common language under every IQ scale. A modern IQ is a z-score rescaled to mean 100 and standard deviation 15 (Wikipedia: Intelligence quotient), so you can always move between them: IQ = 100 + 15 × z. Once you have z, the normal curve gives you the percentile.
Worked examples
- IQ 115: z = (115 - 100) / 15 = +1, about the 84.1th percentile.
- IQ 130: z = +2, about the 97.7th percentile.
- IQ 91: z = -0.6, about the 27.4th percentile.
The 68-95-99.7 rule says about 68% of people fall between z = -1 and z = +1, about 95% between -2 and +2, and about 99.7% between -3 and +3 (the 68-95-99.7 rule).
Common confusions
A z-score depends on the reference group. A z of +1 among adults in one sample is not automatically +1 in another. And in item response scoring, the ability estimate called theta is read much like a z-score but is estimated differently. See standard deviation, the IQ bell curve, or what an IQ of 130 means.
Try one · Logical Reasoning
Which tile completes the second pair?
Tap the option you think is right, or show the answer.
Show the answer
The missing panel shows a large outlined circle, with small solid shapes: a square at the bottom (option 4).
How to solve it
- Compare the first two panels and name exactly what changed.
- The main shape and the small shapes swap forms: the main shape takes the form of the small ones, and the small ones take the form of the main shape.
- Nothing else changes.
- Apply the same change to the third panel: a large outlined square, with small solid shapes: a circle at the bottom.
- So the missing panel shows a large outlined circle, with small solid shapes: a square at the bottom.
That was 1 puzzle. The full test has 25.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- 68-95-99.7 rule. Wikipedia. en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule